How to understand if condition in bash?

I am a little confused about Bash test expression and if test commands:
(1)

#!/bin/bash

count=90

if [ $((count)) ]; then
        echo "True "
else
        echo "False"
fi

Executing it:

# ./test1.sh
True

(2)

#!/bin/bash

count=90

if $((count)); then
        echo "True "
else
        echo "False"
fi

Executing it:

# ./test2.sh  
./test2.sh: line 5: 90: command not found  
False

(3)

#!/bin/bash

count=90

if ((count)); then
        echo "True "
else
        echo "False"
fi

Executing it:

# ./test3.sh
True

My questions are as follows:
a) For test2.sh, why does it complain "command not found"?
b) Although test1.sh and test3.sh outputs the same result, do they have same meanings in if condition?